Question : In a class, the average height of all students is $a$ cm. Among them, the average height of 10 students is $b$ cm, and the average height of the remaining students is $c$ cm. Find the number of students in the class. (Here $a>c$ and $b>c$)

Option 1: $\frac{\left ( a\left ( b-c \right ) \right )}{\left ( a-c \right )}$

Option 2: $\frac{\left ( b-c \right )}{\left ( a-c \right )}$

Option 3: $\frac{\left ( b-c \right )}{10\left ( a-c \right )}$

Option 4: $\frac{10\left ( b-c \right )}{\left ( a-c \right )}$

Question : The volume of a hemisphere is $2425 \frac{1}{2} \mathrm{~cm}^3$. Find its radius.
$\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$

Option 1: 12 cm

Option 2: 10 cm

Option 3: 10.5 cm

Option 4: 9.5 cm

Question : The average height of 30 boys out of a class of 50 is 160 cm. If the average height of the remaining boys is 165 cm, the average height of the whole class (in cm) is:

Option 1: 161

Option 2: 162

Option 3: 163

Option 4: 164

Question : The sum of three fractions A, B and C, A > B > C, is $\frac{121}{60}$. When C is divided by B, the resulting fraction is $\frac{9}{10}$, which exceeds A by $\frac{3}{20}$. What is the difference between B and C?

Option 1: $\frac{1}{15}$

Option 2: $\frac{1}{10}$

Option 3: $\frac{3}{10}$

Option 4: $\frac{7}{15}$

Question : If $M =\left ( \frac{3}{7} \right ) ÷ \left ( \frac{6}{5} \right ) ×\left ( \frac{2}{3} \right ) + \left ( \frac{1}{5} \right ) ×\left ( \frac{3}{2} \right )$ and $N = \left ( \frac{2}{5} \right ) × \left ( \frac{5}{6} \right ) ÷ \left ( \frac{1}{3} \right ) + \left ( \frac{3}{5} \right ) × \left ( \frac{2}{3} \right ) ÷ \left ( \frac{3}{5} \right )$,
then what is the value of $\frac{M}{N}$?

Option 1: $\frac{207}{560}$

Option 2: $\frac{339}{1120}$

Option 3: $\frac{113}{350}$

Option 4: $\frac{69}{175}$

Question : If $\left (a+\frac{1}{b} \right)=1$ and $\left (b+\frac{1}{c} \right)=1$, the value of $\left (c+\frac{1}{a} \right)$ is:

Option 1: 0

Option 2: 1

Option 3: – 1

Option 4: 2